Entanglement – Page 2 – Hard Science Ain't Hard

“Here’s the poly bag wiff our meals, Johnny. ‘S got two boxes innit, but no labels which is which.”
“I ordered the mutton pasty, Jennie, anna fish’n’chips for you.”
“You c’n have this box, Johnny. I’ll take the other one t’ my place to watch telly.”
…
<ring>
” ‘Ullo, Jennie? This is Johnny. The box over ‘ere ‘as the fish. You’ve got mine!”

In a sense their supper order arrived in an entangled state. Our friends knew what was in both boxes together, but they didn’t know what was in either box separately. Kind of a Schrödinger’s Cat situation — they had to treat each box as 50% baked pasty and 50% fried codfish.

But as soon as Johnny opened one box, he knew what was in the other one even though it was somewhere else. Jennie could have been in the next room or the next town or the next planet — Johnnie would have known, instantly, which box had his meal no matter how far away that other box was.

By the way, Jennie was free to open her box on the way home but that’d make no difference to Johnnie — the box at his place would have stayed a mystery to him until either he opened it or he talked to her.

Information transfer at infinite speed? Of course not, because neither hungry person knows what’s in either box until they open one or until they exchange information. Even Skype operates at light-speed (or slower).

But that’s not quite quantum entanglement, because there’s definite content (meat pie or batter-fried cod) in each box. In the quantum world, neither box holds something definite until at least one box is opened. At that point, ambiguity flees from both boxes in an act of global correlation.

There’s strong experimental evidence that entangled particles literally don’t know which way is up until one of them is observed. The paired particle instantaneously gets that message no matter how far away it is.

Niels Bohr’s Principle of Complementarity is involved here. He held that because it’s impossible to measure both wave and particle properties at the same time, a quantized entity acts as a wave globally and only becomes local when it stops somewhere.

Here’s how extreme the wave/particle global/local thing can get. Consider some nebula a million light-years away. A million years ago an electron wobbled in the nebular cloud, generating a spherical electromagnetic wave that expanded at light-speed throughout the Universe.

cats-eye nebula — The Cat’s Eye Nebula (NGC 6543)
courtesy of NASA’s Hubble Space Telescope

Last night you got a glimpse of the nebula when that lightwave encountered a retinal cell in your eye. Instantly, all of the wave’s energy, acting as a photon, energized a single electron in your retina. That particular lightwave ceased to be active elsewhere in your eye or anywhere else on that million-light-year spherical shell.

Surely there was at least one other being, on Earth or somewhere else, that was looking towards the nebula when that wave passed by. They wouldn’t have seen your photon nor could you have seen any of theirs. Somehow your wave’s entire spherical shell, all 10¹² square lightyears of it, instantaneously “knew” that your eye’s electron had extracted the wave’s energy.

But that directly contradicts a bedrock of Einstein’s Special Theory of Relativity. His fundamental assumption was that nothing (energy, matter or information) can go faster than the speed of light in vacuum. STR says it’s impossible for two distant points on that spherical wave to communicate in the way that quantum theory demands they must.

Want some irony? Back in 1906, Einstein himself “invented” the photon in one of his four “Annus mirabilis” papers. (The word “photon” didn’t come into use for another decade, but Einstein demonstrated the need for it.) Building on Planck’s work, Einstein showed that light must be emitted and absorbed as quantized packets of energy.

It must have taken a lot of courage to write that paper, because Maxwell’s wave theory of light had been firmly established for forty years prior and there’s a lot of evidence for it. Bottom line, though, is that Einstein is responsible for both sides of the wave/particle global/local puzzle that has bedeviled Physics for a century.

~~ Rich Olcott

“Watcha, Johnnie, you sure ‘at particle’s inna box?”
“O’course ’tis, Jennie! Why wouldn’t it be?”
“Me Mam sez particles can tunnel outta boxes ’cause they’re waves.”
“Can’t be both, Jessie.”

Maybe it can.

Nobel-winning (1965) physicist Richard Feynman said the double-slit experiment (diagrammed here) embodies the “central mystery” of Quantum Mechanics.

When the bottom slit is covered the display screen shows just what you’d expect — a bright area opposite the top slit.

When both slits are open, the screen shows a banded pattern you see with waves. Where a peak in a top-slit wave meets a peak in the bottom-slit wave, the screen shines brightly. Where a peak meets a trough the two waves cancel and the screen is dark. Overall there’s a series of stripes. So electrons are waves, right?

But wait. If we throttle the beam current way down, the display shows individual speckles where each electron hits. So the electrons are particles, right?

Now for the spooky part. If both slits are open to a throttled beam those singleton speckles don’t cluster behind the slits as you’d expect particles to do. A speckle may appear anywhere on the screen, even in an apparently blocked-off region. What’s more, when you send out many electrons one-by-one their individual hits cluster exactly where the bright stripes were when the beam was running full-on.

It’s as though each electron becomes a wave that goes through both slits, interferes with itself, and then goes back to being a particle!

By the way, this experiment isn’t a freak observation. It’s been repeated with the same results many times, not just with electrons but also with light (photons), atoms, and even massive molecules like buckyballs (fullerene spheres that contain 60 carbon atoms). In each case, the results indicate that the whatevers have a dual character — as a localized particle AND as a wave that reacts to the global environment.

Physicists have been arguing the “Which is it?” question ever since Louis-Victor-Pierre-Raymond, the 7th Duc de Broglie, raised it in his 1924 PhD Thesis (for which he received a Nobel Prize in 1929 — not bad for a beginner). He showed that any moving “particle” comes along with a “wave” whose peak-to-peak wavelength is inversely proportional to the particle’s mass times its velocity. The longer the wavelength, the less well you know where the thing is.

I just had to put numbers to de Broglie’s equation. With Newton in mind, I measured one of the apples in my kitchen. To scale everything, I assumed each object moved by one of its diameters per second. (OK, I cheated for the electron — modern physics says it’s just a point, so I used a not-really-valid classical calculation to get something to work with.)

“Particle”	Mass, kilograms	Diameter, meters	Wavelength, meters	Wavelength, diameters
Apple	0.2	0.07	7.1×10^-33	1.0×10^-31
Buckyball	1.2×10^-24	1.0×10^-9	0.083	8.3×10⁺⁷
Hydrogen atom	1.7×10^-27	1.0×10^-10	600	6.0×10⁺¹²
Electron	9.1×10^-31	3.0×10^-17	3.7×10⁺¹²	1.2×10⁺²⁹

That apple has a wave far smaller than any of its hydrogen atoms so I’ll have no trouble grabbing it for a bite. Anything tinier than a small virus is spread way out unless it’s moving pretty fast, as in a beam apparatus. For instance, an electron going at 1% of light-speed has a wavelength only a nanometer wide.

Different physicists have taken different positions on the “particle or wave?” question. Duc de Broglie claimed that both exist — particles are real and they travel where their waves tell them to. Bohr and Heisenberg went the opposite route, saying that the wave’s not real, it’s only a mathematical device for calculating relative probabilities for measuring this or that value. Furthermore, the particle doesn’t exist as such until a measurement determines its location or momentum. Einstein and Schrödinger liked particles. Feynman and Dirac just threw up their hands and calculated.

Which brings us to the other kind of quantum spookiness — “entanglement.” In fact, Einstein actually used the word spukhafte (German for “spooky”) in a discussion of the notion. He really didn’t like it and for good reason — entanglement rudely collides with his own Theory of Relativity. But that’s another story.

~~ Rich Olcott

Hard Science Ain't Hard

Tag: Entanglement

Oh, what an entangled wave we weave

Think globally, act locally. Electrons do.